Emergence of coherence in the charge-density wave state of 2H-NbSe2
U. Chatterjee1,2*, J. Zhao2,3, M. Iavarone4, R. Di Capua4, J. P. Castellan1,5, G. Karapetrov6, C. D. Malliakas1,7, M. G. Kanatzidis1,7, H. Claus1, J. P. C. Ruff 8,9, F. 1, Weber 5, J. van Wezel1,10, J. C. Campuzano1,3, R. Osborn1, M. Randeria11, N. Trivedi11, M. R. Norman1 and S. Rosenkranz1*
1Materials Science Division, Argonne National Laboratory, , Argonne, IL 60439 USA. 2Department of Physics, University of Virginia, Charlottesville, VA 22904, USA. 3Department of Physics, University of Illinois at Chicago, Chicago, IL 60607, USA. 4Department of Physics, Temple University, Philadelphia, PA 19122, USA. 5Institute of Solid State Physics, Karlsruhe Institute of Technology, P.O. Box 3640, D-‐76021 Karlsruhe, Germany. 6Department of Physics, Drexel University, Philadelphia, PA 19104, USA. 7Department of Chemistry, Northwestern University, Evanston, IL 60208, USA. 8Advanced Photon Source, Argonne National Laboratory, Argonne, , IL 60439 USA. 9CHESS, Cornell University, Ithaca, NY 14853, USA. 10Institute for Theoretical Physics, University of Amsterdam, Tyndall Avenue, 1090 . GL Amsterdam, the Netherlands 11Department of Physics, Ohio State University, Columbus, , OH 43210 USA.
A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the
CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunneling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude that impacts the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states.
Correspondence and requests for materials should be addressed to U.C. ([email protected]) or S.R. ([email protected])
1
The formation of charge-density waves (CDWs) and the CDW order parameter, which is proportional to the energy superconductivity are archetypical examples of symmetry gap Δ, and φ the phase of the CDW, i.e., the location of the breaking in materials, which are characterized by a complex charge modulation with respect to the underlying lattice. It is order parameter. In clean weak-coupling systems, the formation straightforward to realize that there are two ways to destroy the of the amplitude and the establishment of macroscopic phase order parameter — (i) by reducing the amplitude ρ0 through coherence are known to occur simultaneously at the transition excitations across the energy gap and/or (ii) by randomization temperature1,2, but the situation may be dramatically different at of the phase φ either through thermal or quantum fluctuations. strong coupling or in the presence of disorder3-9. Such systems Similar to the case of BCS transitions in clean superconductors, generally exhibit short correlation lengths and a transition the expectation value of δρ in weakly coupled CDW systems temperature that is greatly suppressed from the expected mean- vanishes via (i), as, in general, (ii) is not relevant due to the field value. This opens the possibility for a gap in the electronic large magnitude of the phase stiffness energy1,3. However, spectra to persist in the absence of long-range order over a large strongly coupled CDW systems can be susceptible to strong temperature range and the opportunity to study this so-called phase fluctuations due to their shorter coherence lengths1,4-7. pseudogap behaviour, which has been observed in a wide range To explore this systematically as a function of disorder in a of systems from high-temperature superconductors10-12 to material with a simple electronic and crystal structure, we disordered superconducting thin films13 and cold atoms14, in a investigate pristine and intercalated (with Co and Mn ions) simple system. 2H-NbSe2 samples, where CDW ordering involves strong 15,16 In the CDW state below the transition temperature Tcdw, a electron-phonon coupling . In our investigations, we employ modulation appears in the density of conduction electrons that a combination of experimental probes. Scanning tunneling is accompanied by a periodic lattice distortion1. Although this microscopy (STM) and X-ray diffraction (XRD) are used to lattice distortion leads to an increase in the elastic energy, there is measure the real and momentum space structure of the CDW a net gain in the free energy of the system due to a reduction in order, respectively. Angle resolved photoemission spectroscopy the energy of the electrons via the opening of an energy gap Δ. (ARPES) is employed to investigate the presence of an energy The CDW state is characterized by the order parameter gap in the electronic spectra, which is proportional to the δρ(r) = ρ(r) - ρav(r) = ρ0 cos[q.r +φ(r)], where q is the CDW amplitude of the order parameter, and to infer the existence or wave vector, ρav the average charge density, ρ0 the amplitude of disappearance of phase coherence of the order parameter
Figure 1 | CDW phase transition for pure and intercalated 2H-NbSe2 samples. (a) Intensity of the CDW superstructure peak as a function of T for an x=0 (green) and x=0.0045 (Mn-intercalated, red). Dotted lines are guides to the eye indicating the growth of the CDW order parameter. Arrows mark the estimated Tcdw, which is the interpolation of the linear part to zero. (b) FF divided EDCs for various temperatures at the momentum location shown by the red dot in Fig. 2d. (c) FF divided EDCs for different x at the lowest measured temperatures. The sample with x=0.0165 is intercalated with Co, the others are intercalated with Mn. The corresponding momentum location is shown by the pink dot in Fig. 2d. The red dashed line in b and c shows the energy location of the peak (for T< Tcdw & x
through the presence or absence of sharp coherence peaks in the limited even at our lowest measured temperature. This suggests ARPES spectra. Furthermore, Tcdw is determined by tracking that the process of intercalation gives rise to disorder that the onset of the CDW order parameter in XRD and the CDW- impacts the CDW state, consistent with previous work on 19-22 induced anomaly in transport measurements. Our main results 2H-NbSe2 and other dichalcogenide systems . We can from this extensive set of measurements are as follows. First, nevertheless still identify a CDW transition temperature, even the temperature Tcdw, above which CDW phase coherence is in the intercalated, disordered samples, from a linear destroyed, is suppressed with intercalation x and vanishes at a extrapolation of the temperature dependence of the quantum phase transition (QPT) at xc. Second, the CDW state superstructure intensity, as indicated in Fig. 1a. below Tcdw(x) and x < xc has an energy gap and sharp electronic From our XRD data on samples with different concentrations x excitations. Finally, the CDW energy gap survives above of intercalant ions, we observe that Tcdw is quickly suppressed Tcdw(x) and x > xc in the state which has only short-range CDW (Fig. 1a) as x is increased and beyond xc, superstructure peaks correlations, but the electronic excitations are no longer well- become very broad, indicating that the CDW order becomes defined. short-range.Qualitatively, similar attributes have been identified in resistivity measurements as well: the CDW induced anomaly Results in the resistivity becomes weaker with increasing x, shifts to lower XRD and transport. Previous investigations of the CDW tran- temperatures and eventually disappears beyond xc (see ref. 22, sition in 2H-NbSe2 using neutron and XRD have shown that a Supplementary Note 1 and Supplementary Fig. 2). We note that superstructure with incommensurate wave vector q=(1-δ)a*/3, the effect of doping on the CDW is the same irrespective of where a*=4π/√3a, lattice parameter a=3.44 Å and δ∼0.02, whether the intercalating ion is Mn or Co as observed by STM,
appears below Tcdw=33K (ref. 17). However, the origin of the discussed later. The disappearance of Tcdw naturally points to the CDW and the exact nature of the Nb atom motion involved existence of a QPT at xc. Although our measurements show 16 were only recently established using inelastic X-ray scattering clear signatures of the change in the CDW order across xc, as and superspace crystallography18, respectively. To explore the expected at a QPT, we have not been able to characterize this evolution of the CDW transition with increasing disorder, we QPT in greater detail due to the difficulty in synthesizing use synchrotron XRD and transport measurements on a number samples with dense-enough x values around xc. of intercalated samples (for details, see Methods section and Supplementary Fig. 1). Figure 1a shows the intensity of the Angle-resolved photoemission. To elucidate the evolution of incommensurate superstructure peaks, which is proportional to the electronic structure across Tcdw and xc, we now focus on the the square of the CDW order parameter. For the undoped T- and x-dependent ARPES measurements. We have taken data compound, the superstructure intensity increases continuously over a large region of momentum space in the first Brillouin zone from the temperature-independent background present above (Supplementary Note 2 and Supplementary Fig. 3a). However, Tcdw, as expected for a second-order phase transition. Moreover, we will predominantly be concerned with ARPES data as a the width of this superstructure peak, which is a measure of the function of energy at specific momentum values close to the high inverse of the CDW correlation length, becomes resolution symmetry K-M line (Fig. 2d). The reason for choosing this limited below Tcdw, implying the presence of long-range order particular direction is that the CDW gap is maximum along it (Fig. 1d). For intercalated samples, the XRD superstructure and hence easily detectable by ARPES 23,24. The Fermi function peak exhibits a reasonably sharp onset of intensity (Fig. 1a) as a (FF) at corresponding temperatures is divided out to better function of temperature, but its width (Fig. 1d) is not resolution
Figure 2 | Electronic dispersion exhibiting back bending. (a,b) FF divided EDCs as a function of momentum k along cut 1 (defined in panel d), which is close to the K-M line, for x=0 and at T=26K and T=50K, respectively. Red EDCs are associated with momenta k inside the inner Fermi surface (centred around the K point) starting from the brown dot (shown in d) to the red dot along cut 1, green ones to the remaining k points along cut 1 between the red and black dots. (c) FF divided EDCs for x=0.0165 (Co intercalation) at T=18K, along cut 2, which is along K-M, as shown in d. Red EDCs correspond to k starting from the brown dot inside the inner Fermi surface (centred around the K point) to the pink dot along cut 2, green ones to the remaining k points between the pink and black dots. Blue curves indicate EDCs at the Fermi momentum, the black dots show the locations of the peak and kinks of the EDCs, and the black dashed lines are at the chemical potential. The method for locating the black dots is described in Supplementary Note 5 and Supplementary Fig. 7. (d) Fermi surface plot based on the tight-binding fit to the band structure of 2H-NbSe2 in ref. 24. Black and red arrows denote outer and inner Fermi surface barrels. 3
visualize the existence of the gap Δ from such energy distribution coupling, the electronic dispersion, i.e., the relation between curves (EDCs)25,26. In Fig. 1b, we display the spectral function electronic energy and momentum, is altered from the one in the obtained from the FF-divided EDCs as a function of T for x=0 normal state. In the CDW state with ordering wave vector q, an (raw data, shown in the Supplementary Fig. 3b,c, agree with electronic state with momentum k gets coupled to another with 23,24 previous ARPES studies ). At the lowest temperature (T=26K momentum k+q, and the dispersion is modified to Ek = ½(εk+εk+q) 2 2 ½ < Tcdw=33K), the spectrum exhibits a coherence peak at an ± [¼(εk-εk+q) + Δk ] , where Δk is the energy gap and εk the normal energy below the chemical potential µ, signalling a non-zero state dispersion1,6. The dispersion of the lower branch deviates value of the gap. Unlike superconducting or one-dimensional from εk as εk approaches εk+q, reaches a maximum CDW systems, we find that this gap is centred at positive when εk=εk+q, and then bends back to follow εk+q instead energies, i.e., above µ. This particle-hole asymmetry is clearly (Supplementary Fig. 6 and Supplementary Note 4). This evident from the FF-divided ARPES data shown in Fig. 1b, which bending back effect, commonly known as the Bogoliubov 2 has a negative slope at µ. Consequently, the estimation of the dispersion , occurs in the superconducting state due to electron- energy gap based on the leading edge or by symmetrizing the electron pairing and has been directly observed by ARPES in 31-33 spectra around µ23,24 underestimates the size of the gap. Given cuprates . As shown in Fig. 2a, by monitoring the peak that the minimum of the FF-divided ARPES intensity occurs positions and kinks of the EDCs (see Supplementary Note 5 above µ, we can not determine the exact magnitude of the and Supplementary Fig. 7 for details), it is easy to see that the energy gap, but can only establish its existence and that, in electronic dispersion below Tcdw for x=0 has the expected agreement with recent STM data27, it is larger than estimated by bending back behaviour. And quite remarkably, the bending symmetrisation and leading-edge analysis in previous ARPES back of the dispersion is visible even when the CDW is short- studies. The presence of a particle-hole asymmetric gap is an ranged—(i) in the x=0 sample at T~50K > Tcdw in Fig. 2b and indication that Fermi surface nesting is not important for (ii) an intercalated sample with x~0.0165 > xc at T=18K in driving the CDW in 2H-NbSe2. This is supported by recent Fig. 2c. The presence of CDW gap below and above Tcdw along measurements of soft phonon modes using inelastic X-ray with the persistence of a back bending feature in the electronic scattering16. However, differing conclusions about the role of dispersion naturally suggests that the electron-hole pairs induced 28-30 nesting have been offered in previous ARPES studies . by the CDW persist above Tcdw and beyond xc. We point out that With increase in temperature, the intensity of the coherence similar observations have been made in the pseudogap phase of peak is reduced, but its energy remains the same. Finally, above cuprates where, just as in the superconducting state, a Bogoliubov Tcdw, this peak disappears and remarkably, the spectra become dispersion was found to exist above Tc, which was considered as evidence for pairing without phase coherence34. Taking into almost T independent. Although the spectra for T > Tcdw do not have a discernable peak, they do have a well-defined “kink”, i.e., consideration of all these observations, one can realize that for a sharp change of slope. Closer inspection of Fig. 1b reveals T>Tcdw or x > xc in the (x,T) phase plane of 2H-NbSe2, there are that the location of this kink in the spectra above T is similar electron-hole pairs without coherence, which in turn implies that cdw CDW order parameter vanishes because of phase incoherence. to that of the coherence peaks below Tcdw, as shown by the red dotted line. Although we cannot obtain the exact magnitude of Scanning tunnelling microscopy. So far, we have concentrated the energy gap as a function of T through T , the fact that cdw on the structure and the relevant electronic excitations associated peak/kink structure of the ARPES spectra lies below the with the CDW order in momentum space. To visualize them in chemical potential clearly demonstrates that the energy gap real space, we have performed high-resolution STM measure- persists for T > Tcdw. On the other hand, there is a loss of phase ments as a function of T and x as shown in Fig. 3, where the coherence as indicated by the absence of a peak in these upper panels are STM topographic images, each of which covers spectra. Our ARPES data on 2H-TaS2 exhibits similar features an area of 18.5 nm by 18.5 nm, the second row shows Fourier (Supplementary Note 3 and Supplementary Fig. 5), which in filtered images, and the bottom panels are 2D-Fourier transform turn suggests that these features are generic to quasi two- (FT) images. Figure 3a corresponds to the x=0 sample at T=4.2 dimensional CDW systems. We have also seen similar results K. The almost perfect hexagonal lattice pattern confirms that for other values of x as well in 2H-NbSe2 (Supplementary Fig. our pristine samples are of very high quality and practically 4). Therefore, Tcdw can be identified as the transition from an defect free. A close inspection of the topographic image clearly incoherent, gapped electronic state to a coherent one. This reveals the presence of a locally commensurate CDW pattern that implies that although the CDW order parameter vanishes above repeats after every third lattice spacing; however, phase slips lead Tcdw, its amplitude does not. to the slight incommensuration observed in XRD as well as in the In Fig. 1e, we display the normalized spectral weight as a FT of the STM image shown in Fig. 3i35. The long-range order of function of T (the details of the normalization procedure is both the lattice as well as the CDW is reflected in the sharp peaks described in the caption of Fig. 1). One can clearly observe that observed in the FT image, where the outermost set of the six it decays monotonically with T and vanishes above Tcdw. The x strong peaks correspond to the Bragg peaks of the underlying dependence of the spectra (Fig. 1c) through xc resembles the T lattice, and the innermost ones at ~ 1/3 the wave vector dependence through Tcdw, e.g., the spectrum at the lowest correspond to the lowest order CDW superlattice peaks (Fig. 3, measured temperature progressively loses its peak with Fig. 4). Our topographic as well as FT images of pure samples 27,36-38 increasing x and eventually becomes featureless for x > xc. It are consistent with earlier STM measurements . While the can readily be seen (Fig. 1f) that the x dependence of the CDW order is well visible in the topographic image of the pure normalized coherent spectral weight follows a similar trend as sample, the CDW corrugation in NbSe2 is very small and to the T dependence, that is, it steadily goes down with increasing enhance the subtle features due to CDW modulations, we show x and vanishes above xc. However, a finite energy gap persists Fourier-filtered images in the middle row, panels e-h of Fig. 3. for all x, even beyond xc. In other words, there exists an These images are obtained by applying a mask to the FT image extended region in the (x,T) phase plane of 2H-NbSe2 systems that only retains the region around the lowest-order CDW where the spectral function has an energy gap but no coherence. peaks, e.g. the region between the dash-dotted circles shown in We now look at the details of the (x,T) phase plane in the Fig. 3i, and transforming back to real space. This results in images context of pairing. As a direct consequence of particle-hole of the CDW maxima and allows a direct visualization of the phase 4
Figure 3 | STM data on pristine and intercalated 2H-NbSe2 samples. STM topographic images of (a) x=0 at 4.2 K, (b,c) x=0.0045 (Mn intercalated) at 4.2 K and 77 K, and (d) x=0.04 (Co intercalated) at 4.2 K. The scan areas are 18.5 nm x 18.5 nm. The images have been acquired at V = +50 mV and I = 100 pA. The total z-deflection is 0.6 Å in a,c, 1.0 Å in b, and 1.2 Å in d. (e-h) Fourier filtered images obtained by retaining only the region around the lowest-order CDW peak in the FT images, for example, the region 0.2qBRAGG < q < 0.45qBRAGG indicated by the white dash-dotted circles in i, and transforming back to real space. The dashed white circles in these filtered images show examples of patches with well-defined CDW structures in the intercalated samples. (i-l) 2D-FTs of the topographic images in a-d. The white circles indicate the position of one of the lowest-order Bragg peaks at qBRAGG, blue circles in i-k at ~ 1/3 qBragg indicate the position of the lowest order CDW superlattice peaks. In samples with high CDW disorder, the FT does not show clear CDW peaks but rather a ring-like structure, as indicated by the blue circles in l for Co0.04NbSe2.
Figure 4 | STM FT Profiles. (a) Line profiles of the FT images in Fig. 3i-3l along one of the lattice wavevector directions. The curves have been shifted for clarity. The intensity of each profile has been normalized to the intensity of the Bragg peak. The CDW peak at q=qBRAGG/3 has been fitted with a Gaussian and the fit is superimposed on the FT line profile for each curve. (b) Gaussian fits of the CDW peaks in a normalized to the CDW peak of pure NbSe2. and CDW domain structure. To ensure that the filtered images topographic image is in the range 0.006 Discussion The phase diagram of the CDW correlations in intercalated 2H- NbSe2 shown in Fig. 5 summarizes our results (for simplicity, the superconducting transition observed in all but the very highest doped sample are not shown in this figure). The squares are based on the ARPES spectra that are: (1) coherent and gapped (solid squares) within the triangular region where the CDW order is present, (2) incoherent and gapped (empty squares) outside of this triangle, indicating short-range CDW order instead. The circles correspond to FT-STM data —solid ones within the triangular region where long range CDW order exist and empty ones outside where CDW order is short range. The bow ties indicate the CDW transition temperature determined from transport measurements, and are included for completeness. This phase diagram closely resembles that of the transition from the superconducting to the pseudogap state in cuprates41, and that of the superconducting to insulating transition in disordered systems9,13,42. The experimental observation of the persistence of Overview plot of the results from ARPES, STM, transport, an energy gap and the disappearance of single-particle coherence and XRD measurements. ARPES data points are shown by red squares. across classical or quantum phase transitions seems to be a common Filled squares correspond to the simultaneous presence of the coherence feature of these entirely different systems. The enigmatic pseudogap phase of cuprates is in many ways the most complicated of these peak and an energy gap, empty ones to the presence of only an energy examples, with close proximity to a Mott insulator and various gap. STM data points are shown by blue circles, indicating the presence competing orders. In this respect, the simplicity of 2H-NbSe2 of a CDW. Bow ties denote Tcdw, obtained from transport measurements, studied in this paper makes it possible to focus on a single order marking the transition from a long-range ordered CDW state to a short- parameter, associated with CDW formation, and examine in detail range ordered state as a function of x and T. Extrapolation of this phase how the spectroscopic signatures evolve across the QPT where this line leads to xc ~ 0.013, beyond which there is only short-range order at all ordering is destroyed. measured temperatures. The superconducting transitions, observed for all samples except the very highest doping as listed in Supplementary Methods Table 1, are not shown in this diagram. Intercalated 2H-NbSe2 samples. Cobalt (Co) and manganese (Mn) have been intercalated in pristine 2H-NbSe2 single crystals by adopting the procedures the pure sample (Figs 3i and 4). As x is increased to 0.04, the explained in refs 43,44. XRD patterns show that our intercalated samples have size of the patches with coherent CDW order (Figs. 3d,h) is the same structure as the pristine 2H-NbSe2 samples. The concentration of Co further reduced and the peaks in the FT become even broader, and Mn were determined from energy-dispersive X-ray microanalysis leading to a ring-like structure (Fig. 3l). In Fig. 4a, we present measurements. While performing energy-dispersive X-ray microprobe analysis the line profiles of the FT in Fig. 3i-l along the atomic wave on intercalated samples, we have randomly chosen different regions of the vectors as a function of doping, and in Fig. 4b we display the samples and found that the atomic concentrations of Co and Mn remain almost the same, meaning there is no evidence for clustering on the length scale of Gaussian fits to these CDW peaks (Supplementary Note 6), 45 from which we clearly see the broadening of the CDW peak 100 nm. This is substantiated by previous EXAFS measurements . with doping. These results simply relate to the fact that the The superconducting critical temperature (Tc) for pristine 2H-NbSe2 samples is ~7.2K, and it was previously shown that Tc gets suppressed due to CDW coherence length decays with increasing x and eventually intercalation46. Our magnetization versus temperature measurements for becomes short-range, consistent with our ARPES and XRD different samples show sharp superconducting transitions (Supplementary observations. We note that these observations are independent Figure 1), which further support that our intercalated samples are homogeneous. of the intercalating ion, see Supplementary Note 7 and Supplementary Table 1 lists details of all the samples used in this study. Supplementary Figs 8,9. STM observations of domain-like structures having well defined CDW order, similar to those Transport measurements. The temperature-dependent resistivity of the single crystals was measured using regular four-terminal transport measurement shown in Fig. 3f, have been reported in a number of disordered 39,40 technique performed with a Physical Property Measurement System by dichalcogenide systems . Quantum Design equipped with external device control option. Keithley We now focus on STM data for T > Tcdw (Fig. 3c,g,k) 6220 current source and Keithley 2182 nanovoltmeter were used to apply a corresponding to the x=0.0045 sample at T=77K >Tcdw=20K. DC current and measure the voltage drop, respectively. Although weak in intensity, well-defined CDW modulations XRD measurements. Synchrotron XRD experiments were performed at the survive in various regions, as best seen in the Fourier-filtered Advanced Photon Source, Argonne National Laboratory. Data were taken in image Fig. 3g, and the FT image (Fig. 3k) still clearly shows transmission geometry with 22.3keV X-rays on the 11-ID-D beamline using a broad CDW peaks, indicating the persistence of short-range Ketek Silicon Drift point detector and on the high-energy station of beamline 6-ID-D with 80keV X-rays and a Pilatus 100K area detector. In both setups, CDW correlations to temperatures well above Tcdw. In the pure sample, we observe very weak CDW modulations localized the samples were mounted on the cold head of a closed-cycle helium displex around the impurities up to 45 K (Supplementary Figure 10a). refrigerator and sealed inside a Be-can with He exchange gas. Given the small amount of defects and the weak modulation, ARPES measurements. ARPES measurements were carried out at the PGM only very weak CDW peaks are observed in the 2D-FT. We do beamline of the Synchrotron Radiation Center, Stoughton, WI, and at the not observe any sign of CDW modulations in real space or in SIS beamline of the Swiss Light Source, Paul Scherrer Institut, Switzerland, utilizing Scienta R4000 analyzers and 22 eV photons for all the 2D-FT at 77 K (Supplementary Fig. 10b). This can be measurements. 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Valla, T., et al., Quasiparticle Spectra, Charge-Density Waves, Superconductivity, and Electron-phonon Coupling in 2H-NbSe2. Phys. Rev. Lett. Acknowledgements. 92, 086401 (2004). Work at Argonne (U.C., J.Z., J.P.C., C.D.M., M.G.K., H.C., J.P.C.R., F.W., J.C.C, 16. Weber, F., et al., Extended Phonon Collapse and the Origin of the Charge- R.O., M.R.N., S.R.) was supported by the Materials Science and Engineering Density Wave in 2H-NbSe2. Phys. Rev. Lett. 107, 107403 (2011). Division, Basic Energy Sciences, Office of Science, U.S. Dept. of Energy. Work at 17. Moncton, D.E., Axe, J. D. and DiSalvo, F. J., Study of superlattice formation in Temple University (M.I.) and Drexel University (G.K.) was supported as part of the 2H-NbSe2 and 2H-TaSe2 by neutron scattering. Phys. Rev. Lett. 34, 734-737 (1975). Center for the Computational Design of Functional Layered Materials, an Energy 18. Malliakas, C. D., Kanatzidis, M. G., Nb-Nb Interactions Define the Charge Frontier Research Center funded by the U.S. DOE, BES under Award DE- Density Wave Structure of 2H-NbSe2, J. Am. Chem. Soc. 135, 1719 (2013). SC0012575. J.v.W. acknowledges support from a VIDI grant financed by the 19. Mutka, H., et al., Charge-density waves and localization in electron-irradiated Netherlands Organization for Scientific Research (NOW). M.R. was supported by 1T-TaS2. Phys. Rev. B. 23, 5030–5037 (1981). the DOE-BES grant DE-SC0005035. NT was supported by the U.S. DOE, Office of 20. Tao, W. H., et al., Effect of Te doping on superconductivity and charge-density Science, Grant DE-FG02-07ER46423. The Synchrotron Radiation Center is wave in dichalcogenides 2H-NbSe2-xTex (x = 0, 0.1, 0.2). Chinese Phys. 16, supported by the University of Wisconsin, Madison. Synchrotron x-ray scattering 2471-2474 (2007). experiments were carried out at the Advanced Photon Source, which is supported by 21. Mutka, H., Superconductivity in irradiated charge-density-wave compounds 2H- the DOE, Office of Science, BES. We thank Ming Shi for his support with the NbSe2, 2H-TaS2, and 2H-TaSe2. Phys. Rev. B 28, 2855–2858 (1983). experiments at the Swiss Light Source, Paul Scherrer Institut, Switzerland, and D. 22. Iavarone, M., et al., STM studies of CoxNbSe2 and MnxNbSe2. Journal of Phys: Robinson and K. Attenkofer for their support with the X-ray diffraction Conf. Series 150, 052073 (2009). measurements at the Advanced Photon Source, Argonne National Laboratory. 23. Borisenko, S. V., et al., Two Energy Gaps and Fermi-Surface “Arcs” in NbSe2. Phys. Rev. Lett. 102, 166402 (2009). 24. Rahn, D. J., et al., Gaps and kinks in the electronic structure of the Author Contributions. superconductor 2H-NbSe2 from angle-resolved photoemission at 1 K. Phys. Rev. U.C. and S.R. proposed the research project, U.C. and J.Z. carried out the ARPES B 85, 224532 (2012). measurements and analysis of the ARPES data. J.P.C., J.P.C.R., F.W., R.O. and 25. Damascelli, A., Hussain, Z. and Shen, Z. X., Angle resolved photoemission S.R. carried out the XRD measurements and analysis of the XRD data. M.I., R.D.C., studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473-541 (2003). and G.K. carried out the STM, transport measurements and analysis of STM and 26. Campuzano, J.C., Norman, M.R. and Randeria, M. in Physics of Superconductors, transport data. M.I., G.K., C.D.M. and M.G.K. synthesised high quality pristine and intercalated NbSe2 samples. H.C. conducted the superconducting SQUID vol. II (eds Bennemann, K.H. & Ketterson, J.B.) 167-273 (Springer, Berlin, 2004). 27. Soumyanarayanan, A. et al., Quantum phase transition from triangular to stripe measurements on the samples to determine their superconducting critical charge order in NbSe2, Proc. Natl. Acad. Sci. 110, 1623-1627 (2013). temperatures. U.C., J.v.W., M.R., N.T., M.R.N., and S.R. wrote the manuscript. All 28. Tonjes, W. C., et al., Charge-density-wave mechanism in the 2H-NbSe2 authors discussed the results and contributed to the manuscript. family:angle-resolved photoemission studies, Phys. Rev. B 63, 235101 (2001). 29. Straub, Th., et al., Charge-Density-Wave Mechanism in 2H-NbSe2: photoemission results, Phys. Rev. Lett. 82, 4504-4507 (1999). Additional Information 30. Shen, D. W., et al., Primary Role of the Barely Occupied States in the Charge Supplementary Information attached Density Wave Formation of NbSe2, Phys. Rev. Lett. 101, 226406 (2008). 31. Matsui, H., et al., BCS-Like Bogoliubov Quasiparticles in High-Tc Competing financial interests: The authors declare no competing Superconductors Observed by Angle Resolved Photoemission Spectroscopy. financial interest Phys. Rev. Lett. 90, 217002 (2003). 32. Campuzano, J. C., et al., Direct observation of particle-hole mixing in the superconducting state by angle-resolved photoemission. Phys. Rev. B 53, R14737-R14740 (1996). 7 Supplementary Information x=0 x=.013, Co intercalation x=.0045, Mn intercalation M ( a.u ) ! 3 4 5 6 7 T(K)! Supplementary Figure 1 | Magnetization versus temperature curves for pristine and intercalated 2H-NbSe2 samples. Superconducting transition for different values of x. 8 a" b" 0.01 /dT ) (50K) ρ / NbSe ρ 2 ( d Mn0.0012NbSe2 1E-3 Mn0.0045NbSe2 Co0.013NbSe2 10 20 30 40 50 T(K) ' g.'S2' Supplementary Figure 2 | Transport data on pure and intercalated samples. (a) Resistivity normalized to its value at 50K for x=0, 0.0012 (Mn intercalated), 0.0045 (Mn intercalated) and 0.013 (Co intercalated). (b) Temperature derivative of the ρ vs T plot of the data presented in (a). Arrows indicate the CDW transition temperature. The sample with x=0.013 does not show any appreciable change in the first derivative of the resistivity data. 9 a! b! 1.0 Γ x=0$ 26K 0.8 30K 35K 40K 45K 0.6 50K 60K Ky! 0.4 -0.10 0.00 Energy (eV)! Cut! 0.2 c! 2! M K x=0, T=26K Inner! Cut 1! x=.0009,T=23K 0.0 (Mn intercalation) FS ! x=.0045, T=18K barrel! Outer! (Mn intercalation) FS ! x=.0165, T=18K (Co intercalation) barrel! x=.0192,T=18K (Mn intercalation) Kx! -0.10 0.00 Energy (eV)! Supplementary Figure 3 | Raw ARPES data: (a) Raw ARPES intensity map at zero binding energy (integrated over an energy window of 10 meV) as a function of kx and ky for an x=0 sample exhibiting double walled Fermi surfaces centered around the Γ as well as the K point. As shown in Fig. 2d, cut 1 is along the red line, while cut 2 is along the blue line. Data in Figs. 2a, 2b are taken along cut 1 and Fig. 2c along cut 2. Raw EDCs corresponding to the Fermi function divided ones in (b) Fig. 1b and (c) Fig. 1c. Black dotted lines denote the location of the chemical potential. 10 a! b! 23K 45K 28K 40K x=0.0009! x=0.0192! Mn#intercala+on# Mn#intercala+on# -0.15 -0.10 -0.05 0.00 -0.15 -0.10 -0.05 0.00 Energy (eV)! Energy (eV)! Supplementary Figure 4 | Fermi function divided ARPES data for two different intercalated samples. Temperature dependent Fermi function divided ARPES EDCs for (a) x=0.0009 (taken at the red dot in Fig. 2d) and (b) x=0.0192 (taken at the blue dot in Fig. 2d). Black dotted lines denote the location of the chemical potential. Red dotted lines are used to indicate the energy gap defined as the location of either the peak or kink (i.e., discontinuous change in slope) in the spectrum. 11 40K 60K 75K 90K 2H#TaS2' Intensity (a.u.) 100K -0.10 0.00 Energy (eV) Supplementary Figure 5 | Fermi function divided ARPES data from 2H-TaS2. Temperature dependent Fermi function divided ARPES EDCs for 2H-TaS2. ARPES data correspond to the momentum location at which the K-M line intersects the Fermi surface. Like in 2H-NbSe2 (Fig. 1b of main manuscript), here one can also identify a gap and peak in the spectrum for T 12 ) ρ a! 2π/q u n 2ρ0"av a Charge Density ( Position (r) upper b! branch (empty) εk 2Δ EF Energy kF lower branch (filled) q=2kF -1 0 1 Wavevector k (π/a) Supplementary Figure 6 | Electronic dispersion in the CDW state associated with a Peierls distortion in a one-dimensional system. (a) A cartoon of one-dimensional CDW order in real space and (b) the corresponding electronic dispersion in momentum space in the normal state (black dotted line) and in the CDW state (red lines). 13 Intensity (arb units) ' '' -0.10 0.00 Energy (eV) Supplementary Figure 7 | Identification of peaks and kinks in the ARPES spectra. Demonstration of how dots are selected, particularly when the spectra are not associated with sharp peaks, to investigate bending back of the electronic dispersion in Fig. 2. In particular, we have chosen Fig. 2b in which peak structures of the spectra are not very clear. 14 (a)$ x=0.003$$ (b)$ x=0.003$$ (c)$ x=0.003$$ (Co$intercala4on)$ (Co$intercala4on)$ (Co$intercala4on))$ Supplementary Figure 8 | STM of Co0.003NbSe2. (a) STM topography image acquired with V=50 mV and I=100 pA. Scan area is 24 nm x 24 nm (scale bar: 2nm). (b) Fourier filtered image of the topography shown in (a). (c) 2D-FT of the image in (a). 15 (a)$ (b)$ x=0.0045$(Mn$intercala4on)$ x=0.003$(Co$intercala4on)$ Supplementary Figure 9 | STM Fourier Transform Profiles for different dopants. (a) Line profiles of the FT of the Mn0.0045NbSe2 image (Fig. 3(j) of main text) and the FT of the Co0.003NbSe2 image (Supplementary Figure 8c), along one of the lattice wavevector directions. The curves have been shifted for clarity. The intensity of each profile has been normalized to the intensity of the Bragg peak. The CDW peak at q=qBRAGG/3 has been fitted with a Gaussian and the fit is superimposed on the FT line profile for each curve. (b) Gaussian fits of the CDW peaks in Mn0.0045NbSe2 and Co0.003NbSe2 compared to the CDW peak in pure NbSe2. 16 (a)$ x=0$ T=45$K$ (b)$ x=0$ T=77$K$ Supplementary Figure 10 | STM topography of 2H-NbSe2. STM topography images of pure NbSe2 above the temperature for long range order. Scan areas for both images are 13.5 nm x 13.5 nm (scale bars: 2 nm). Tunneling conditions are: V=50 mV and I =100 pA. (a) T=45 K, (b) T=77 K. 17 x Type of intercalating ion Tc Tcdw 0 None 7.2K 32.2K 0.0009 Mn 6.5K 29K 0.0012 Mn 5.6K 26.6K 0.0045 Mn 3.4K 23K 0.0192 Mn <1.8K 0K 0.013 Co 5.6K 0K 0.0165 Co 4.7K 0K 0.04 Co 3.1K 0K Supplementary Table 1 | Sample details Concentration of the intercalation ion (x), type of the intercalating ion, superconducting critical temperature (Tc) and Tcdw for the samples used in this paper. 18 Supplementary Note 1 Determination of Tc We determine the CDW transition temperature Tcdw from the CDW induced anomaly in the transport measurements and from the temperature dependence of the CDW order parameter obtained from XRD measurements. We find that these different measurements provide values for Tcdw that are close to each other. Supplementary Figure 2 shows resistivity ρ vs temperature T for four samples with x=0; x=0.0012, x=0.0045 (intercalated with Mn); and x=0.013 (intercalated with Co), normalized to their individual resistivity at 50K. The derivatives dρ/dT vs T (Supplementrary Figure 2b) for the three samples with x < xc exhibit clear anomalies, which we identify as the CDW transition temperature Tcdw. These transition temperatures agree with the transition temperatures determined as described in the main text from the temperature dependence of the superlattice reflections measured with XRD. The fourth sample with x > xc does not show any anomaly. Supplementary Note 2 Raw ARPES data Supplementary Figure 3a shows the raw ARPES intensity map at zero binding energy (integrated over an energy window of 10 meV) as a function of kx and ky. Raw ARPES spectra corresponding to the Fermi function divided ones in Figs. 1b,c are displayed in Supplementary Figures. 3b,c. One can readily observe the energy bands that form two barrels around the K point – the low energy peak/kink corresponds to the inner barrel while the high binding energy “hump” corresponds to the outer barrel (Fig. 2d, Supplementary Figure 3a). For our discussions, we have focused on data in the vicinity of the inner barrel. Supplementary Figure 3b shows a quasiparticle peak that appears at positive binding energy, gets weaker with T, and eventually disappears above Tcdw. Similarly, the spectra in Supplementary Figure 3c lose their peak with increasing x, and beyond xc the peak vanish. Figure 1b showed the temperature evolution of ARPES spectra across the CDW phase transition. Supplementary Figure 4a shows similar data, i.e. Fermi function divided EDCs taken at the red dot in Figs. 2d, for x=0.0009 (Mn intercalation) at temperatures below and above Tcdw. The low temperature spectrum has both an energy gap and a peak, while for T > 19 Tcdw, the peak disappears but the energy gap remains. Supplementary Figure 4b shows Fermi function divided EDCs at T=28K and 40K for x=0.0192 (Mn intercalation) > xc, taken at k marked by the blue dot in Fig. 2d. In contrast to Fig. 1b and Supplementary Figure 4a, there is no signature of a peak in Supplementary Figure 4b even at the lowest measured temperatures. Rather there is a kink (marked by the red dotted line) at positive binding energy, with the minimum of the spectrum above the chemical potential, again indicating the presence of an energy gap. Supplementary Note 3 Loss of coherence at the CDW phase transition in 2H-TaS2 2H-TaS2, like 2H-NbSe2, exhibits CDW ordering, but with higher transition temperature (Tcdw ~70K) (Ref. 1). Our ARPES data measured on 2H-TaS2 (Supplementary Figure 5) shows similar features as that for 2H-NbSe2. The data for T Supplementary Note 4 Energy gap and backbending of the electronic dispersion in the CDW state In contrast to superconductors where there is electron-electron pairing, a CDW state is associated with a coupling between electrons and holes, and this is manifested in the electronic dispersion, i.e. the relation between the electronic energy and momentum, below Tcdw. As a consequence, the electronic dispersion in the CDW state gets modified from the 3,4 one in the normal state, i.e. for T> Tcdw, and this can be written as : 2 2 ½ Ek = ½(εk+εk+q) ± [¼(εk-εk+q) + Δk ] where Δk is the momentum dependent energy gap, εk is the normal state dispersion (T>Tcdw) and q is the CDW wavevector. For simplicity, we consider CDW ordering in a one- dimensional system, noting that there are some important differences between CDW order in 1D and 2D systems, like the fact that the energy gap in the 2D case may be centered away from the Fermi level (as we observe to be the case in 2H-NbSe2). Our primary focus 20 here is to illustrate the salient experimental signatures associated with the formation of charge order irrespective of dimensionality. The most important of these are the opening of a gap and the related backbending of the electronic dispersion, accompanied by coherence factors, which indicate the amount of mixing between the coupled bands that influence the intensity of the experimental signal. These features are manifested in the 1D case in precisely the same manner as they are in a 2D charge ordered state. Supplementary Figure 6a shows a schematic of the real space structure of a 1D CDW state, which can be understood as a Peierls instability with a CDW wave vector q=2kf, where kf is the Fermi momentum. The electronic dispersion of this CDW state, using the equation above, is displayed as the red curves in Supplementary Figure 6b. Ek consists of two branches, which instead of crossing the chemical potential bend downwards/upwards at kf. This characteristic bending back of the dispersion provides a direct signature of the electron-hole coupling in the CDW state, with the difference in energy between the lower and the upper branches at kf being twice the energy gap, Δ. Supplementary Note 5 Identification of peaks and kinks in ARPES data The black dots in Fig.2 correspond to either peaks or the locations of discontinuity, i.e., kinks, in the Fermi function divided ARPES spectra. The procedure for determining the location of the black dots in Figure 2 of the main manuscript is as follows: (i) Whenever there is a discernable peak in the spectrum, it is quite straightforward to select the location of the peak and the black dot corresponds to the peak position. (ii) When there is no well- defined peak we use a simple method: we approximate the leading edge of the spectrum by a straight line and the dot corresponds to that particular energy value at which the straight line starts to deviate from the spectrum. We have considered the data displayed in Fig. 2b, in which the peaks of the spectra are not pronounced, and demonstrated how to determine the locations of black dots in Supplementary Figure 7. Supplementary Note 6 STM Fourier Transform profiles In Fig. 3 the 2D-FT of the STM topographic images for samples with different intercalation density are shown. All the images show hexagonal spots corresponding to the Bragg peaks 21 and the CDW peaks. In Figure 4a, line cuts of the FT along the lattice ordering vector are reported. The intensity of each line cut has been normalized to the intensity of the Bragg peak. In order to quantify the broadening of the CDW peak with the density of intercalating ions (Mn/Co) and the temperature, we fitted the CDW peak with a Gaussian function of the ! $ # & = + A − 2 2 form: y y0 # &exp( 2 x w ) , where y0 is the background of the FT line cut and w # w π & " 2 % is a width parameter. Figure 4b shows the CDW peak Gaussian fits for the different line cuts. From this figure we observe that the intensity of the CDW peak decreases and the peak broadens with increasing intercalant doping and with increasing temperature. The broadening of this peak measures the loss of translational order. In the case of pure 2H-NbSe2 above the temperature for long range order, we do observe weak CDW modulations localized around impurities (Supplementary Figure 10a). However, this modulation is very weak and the peaks in the FT are not clearly defined. At T=77 K we do not observe any CDW modulations in real space and any CDW peaks in the FT within our resolution, given the low defect density of our samples (Supplementary Figure 10b). Supplementary Note 7 Effect of different dopants on the CDW order of intercalated 2H-NbSe2 Co and Mn intercalated 2H-NbSe2 crystals with similar doping levels have been characterized with STM. In Supplementary Figure 8 an STM topography image is reported for Co0.0030NbSe2, together with the FT and the Fourier filtered image. The Fourier filtered image reveals that the CDW lattice forms patches very similar to those obtained in Mn0.0045NbSe2. The line profile of the FT in Supplementary Figure 8c along a crystal lattice direction is compared with the one obtained for Mn0.0045NbSe2 (Supplementary Figure 9a), and the fits of the CDW peaks for the two samples are reported in Supplementary Figure 9b. These measurements show that the effect of Co and Mn on the CDW order is the same. 22 Supplementary References 1. McMillan, W. L., Microscopic model of charge-density waves in 2H-TaSe2. Phys. Rev. B. 16, 643 –650 (1977). 2. Wagner. K. E., et al., Tuning the charge density wave and superconductivity in CuxTaS2, Phys. Rev. B 78, 104520 (2008). 3. Gruner, G., Density waves in solids. (Perseus Publishing, Cambridge, 1994). 4. Rossnagel, K., On the origin of charge-density waves in select layered transition-metal dichalcogenides. J. Phys.: Condens. Matter 23, 213001 (2011 23